Vacancies in ordered and disordered binary alloys treated with the cluster expansion

Abstract

First-principles investigations of the thermodynamics of binary alloys using a cluster expansion have so far neglected the presence of vacancies. Here, we invoke a local cluster expansion as a perturbation to the standard binary cluster expansion to model the equilibrium vacancy concentration in a binary alloy as a function of temperature and alloy composition. We apply this approach to a first-principles investigation of the fcc Al 1−x Li x alloy ͑for x less than 0.3͒ which at x = 0.25 exhibits L1 2 superstructure ordering. The equilibrium vacancy concentration is predicted to be sensitive to the bulk alloy composition x in the ordered L1 2 phase, varying by more than an order of magnitude in a narrow interval of x at intermediate temperatures. Both in the solid solution and in the ordered L1 2 phase, the vacancy prefers a nearest neighbor shell rich in aluminum. In the L1 2 ordered phase, the vacancy predominantly occupies the lithium sublattice. The type of short-range order around a vacancy should affect the mobility of the constituents of the alloy and hence its interdiffusion coefficient.

Ab initioprediction of vacancy properties in concentrated alloys: The case of fcc Cu-Ni

“…We consider the problem of vacancy formation energies in disordered alloys, a problem that recently is receiving increased attention [27,28,31,33]. We limit ourselves initially to configurationally random alloys, i.e., the reference state is the configurationally random state without vacancies.…”

“…Just considering the nearest neighbor shell in fcc solid solutions alone gives 144 distinct configurations [47] in a binary alloy. Therefore, it is usually more efficient to compute neighborhood dependent vacancy formation enthalpies through cluster expansions [31][32][33].…”

“…Initially using empirical potentials [22][23][24][25], and later through ab initio approaches, both through supercell calculations [26][27][28][29] and ab initio based cluster expansions [30][31][32][33], it has been established that the local atomic environment around a vacancy plays a significant role. While the influence of vacancies on phase stability [30,34] and kinetics [31][32][33] received some attention for Al-Ni [30], Sc-S [34], and Al-Li [31][32][33] alloys, the actual vacancy properties in specific alloys were mostly neglected with the exception of an empirical potential study of Cu-Ni alloys by Zhao et al [24]. In the latter study [24] vacancies were studied with an embedded atom method (EAM) potential and structural relaxation, vibrational, and configurational effects were included.…”

An intuitive and efficient method for cell voltage prediction of lithium and sodium-ion batteries

“…Although this may appear much easier to conduct than experiments, the procedure still requires a significant amount of work: both the alkali-rich and the alkali-poor compositions have to be computed within a reasonable numerical accuracy for their energy difference to be meaningful, and sometimes with functionals that go beyond the usual local density approximation 8 or generalized gradient approximation 9,10 . While this is certainly tractable for a quite large set of compounds 5,11 , it becomes limited or prohibitive when realistic materials including defects, disorder or dopants must be studied 12,13 . Above all, first-principles calculations are not straightforwardly utilizable by non informed users.…”

Cluster Expansions for Thermodynamics and Kinetics of Multicomponent Alloys

“…In particular, the generalized Ising model for binary alloys cannot be extended easily to multinary alloys. [37] The specific treatment in the literature of vacancy mediated diffusion in alloys [21,38,39] too, is scant and not very detailed on practical implementation. In the current work we try to present a comprehensive and detailed formalism that trivially extends to multi-component alloys.…”